Affine representations of fractional processes with applications in mathematical finance

TL;DR

This paper introduces a novel affine representation for certain fractional processes, enabling more tractable financial modeling by addressing computational and calibration challenges inherent in their non-Markovian nature.

Contribution

The authors develop an affine functional representation for fractional processes, facilitating easier computation and application in financial models.

Findings

Representation as linear functionals of infinite dimensional affine processes

Construction of tractable financial models with fractional features

Addresses computational and calibration difficulties in fractional processes

Abstract

Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and practical difficulties in computation and calibration. To address these issues, we show that a certain class of fractional processes can be represented as linear functionals of an infinite dimensional affine process. This can be derived from integral representations similar to those of Carmona, Coutin, Montseny, and Muravlev. We demonstrate by means of several examples that this allows one to construct tractable financial models with fractional features.